Question

Using pythagorean theorem find a, and b, where a is twice of b and the hypotonuse is 5√5

Answer 1

The pythagoras theorem is
`a^(2) + b^(2) = c^(2)` where C is the hypotenuse.

Since a is twice of b,
a = 2b

The hypotenuse is C = 5√5.

Let's put this into the pythagoras equation


`( 2b)^(2) + b^(2) = (5 √(5))^(2)`


`5b^(2) = (125)`


`b^(2) = 25`


`b=5`

since we know a=2b, then a = 2(5)
a=10
`since we know a=2b, then a = 2(5)`

Answer 2

Measure of Hypotaneous = 5√5

And it's already given that b = 2a

By using pythagoras theorem:

a²+ b² = (5√5)²

Let's substitute for b as 2a in above equation we'll get:

a² + (2a)² = (5√5)²

a² + 4a² = 125
5a² = 125
a² = 25
a = √25 = 5


Therefore,
a= 5
and
b = 2a = 2(5) = 10.